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Bootstrapping the O(N) Vector Models

We study the
conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous
upper bounds on the scaling dimensions of the first O(N) singlet and symmetric
tensor operators appearing in the \phi_i x \phi_j OPE, where \phi_i is a
fundamental of O(N). Comparing these bounds to previous determinations of
critical exponents in the O(N) vector models, we find strong numerical evidence
that the O(N) vector models saturate the bootstrap constraints at all values of
N. We also compute general lower bounds on the central charge, giving numerical
predictions for the values realized in the O(N) vector models. We compare our
predictions to previous computations in the 1/N expansion, finding precise
agreement at large values of N.